Organic-inorganic halide perovskites possess unique electronic configurations and high structural tunability, rendering them promising for photovoltaic and optoelectronic applications. Despite significant progress in optimizing the structural characteristics of the organic cations and inorganic framework, the role of organic-inorganic interactions in determining the structural and optical properties has long been underappreciated and remains unclear. Here, by employing pressure tuning, we realize continuous regulation of organic-inorganic interactions in a lead halide perovskite, MHyPbBr3 (MHy+ = methylhydrazinium, CH3NH2NH2+). Compression enhances the organic-inorganic interactions by strengthening the Pb-N coordinate bonding and N-H···Br hydrogen bonding, which results in a higher structural distortion in the inorganic framework. Consequently, the second-harmonic-generation (SHG) intensity experiences an 18-fold increase at 1.5 GPa, and the order-disorder phase transition temperature of MHyPbBr3 increases from 408 K under ambient pressure to 454 K at the industrially achievable level of 0.5 GPa. Further compression triggers a sudden non-centrosymmetric to centrosymmetric phase transition, accompanied by an anomalous bandgap increase by 0.44 eV, which stands as the largest boost in all known halide perovskites. Our findings shed light on the intricate correlations among organic-inorganic interactions, octahedral distortion, and SHG properties and, more broadly, provide valuable insights into structural design and property optimization through cation engineering of halide perovskites.